Question

\(\left(\dfrac{2}{3}x^2-\dfrac{1}{2}y\right)^3\)

Answer 1

\(\left(\dfrac{2}{3}x^2-\dfrac{1}{2}y\right)^3\)

\(=\left(\dfrac{2}{3}x^2\right)^3-3\cdot\left(\dfrac{2}{3}x^2\right)^2\cdot\dfrac{1}{2}y+3\cdot\dfrac{2}{3}x^2\cdot\left(\dfrac{1}{2}y\right)^2-\left(\dfrac{1}{2}y\right)^3\)

\(=\dfrac{8}{27}x^6-\dfrac{2}{3}x^4y+\dfrac{1}{2}x^2y^2-\dfrac{1}{8}y^3\)